Advanced numerical and theoretical methods for photonic crystals and metamaterials
Photonic crystals Metamaterials Waves
IOP Publishing
2016
EISBN 9781681743011
Foreword.
1. Maxwell equations.
1.1. Macroscopic Maxwell equations.
1.2. Symmetry properties.
1.3. Harmonic scattering by a bounded obstacle.
1.4. Covariant formulation.
1.5. Maxwell equations using forms
2. Bloch waves.
2.1. The periodic structure.
2.2. Computation of band structures.
2.3. Topological aspects of Bloch theory.
3. Modal methods
3.1. Multiple scattering theory.
3.2. Fourier modal method
4. Direct space discretization.
4.1. Introduction.
4.2. Differentiation matrices.
4.3. Finite differences in frequency domain.
4.4. Time-dependent problems
5. Homogenization and transformation optics.
5.1. Homogenization.
5.2. Transformation optics.
This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.
1. Maxwell equations.
1.1. Macroscopic Maxwell equations.
1.2. Symmetry properties.
1.3. Harmonic scattering by a bounded obstacle.
1.4. Covariant formulation.
1.5. Maxwell equations using forms
2. Bloch waves.
2.1. The periodic structure.
2.2. Computation of band structures.
2.3. Topological aspects of Bloch theory.
3. Modal methods
3.1. Multiple scattering theory.
3.2. Fourier modal method
4. Direct space discretization.
4.1. Introduction.
4.2. Differentiation matrices.
4.3. Finite differences in frequency domain.
4.4. Time-dependent problems
5. Homogenization and transformation optics.
5.1. Homogenization.
5.2. Transformation optics.
This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.
